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Unformatted text preview: MATH132 LECTURE 1,3 FINAL EXAM
SPRING 2007 Thursday, May 17, 2007 5:05pm—7205pm INSTRUCTOR: MYOUNGJEAN BAE YOUR NAME: Part I. Multiple choice/ Short answer questions 'o Please use the answer sheet provided with the exam to write your final answer. c For part L you only need to write the ﬁnal answer. No detailed work is required to
be shown. c There are 15 questions. l.Choose all graphs which describe a function that has its inverse function.(5points) (0x) \ ___...——_~._.~.. Hf Doma‘ml 5(2‘1 2.The following is a graph of a linear function fr) = ma: + b for some constants m and b.
' From the graph, ﬁnd m(the slope) and b(the y—intercept) of the linear function. Write your
answer.(5points) 3.Suppose a, medical researcher puts a colony of bacteria weighing 1 gram in a large petri
dish. Assume that these bacteria reproduce in such a Way that their number triples every
30 minutes. HOW much will the colony of bacteria weigh after 5 hours? Write your answer. (4points) 4. Let {a1,a2,a3,m g1”,  ~  be an arithmetic sequence. If a3 = 5 and (112 = 23, then
what is a14?(5points) Cn
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00 (a) 24 (b) 2 [5 — 6]The following shows the 10point test scores of 40 students of a' class. x X x
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5 5. What is the mode of the data above?(5points) 6.What is the 25th percentile of the data above?(5points) (a) 1 (b) 2 (c) 3 (d) 4 (e) 5 7.Carol,a zoologist, is studying ecological system of a forest in Austrailia. As a part of
the study, she is trying to estimate the number of koalas. She and her research team mem—
bers set some traps on eucalyptus trees and caught 43 koalas. After tagging the koalas,
they released the koalas unharmed. Two weeks later, the team set some traps again and
caught 51 koalas. And two of the trapped koalas were tagged indicating that they had been
trapped two weeks‘earlier. Based on the result, what is the best estimate of the number of
koalas in the forest? Write your answer as an integer(whole number).(6points) 8,1n Ritzy county, the average annual household income is $95, 000. In neighboring Normal
County, the average annual household income is $67,000. If the number of house hold in
Ritzy county is 5770 and the number of household in Normal County is 2210, then what is
the average annual household income in the twocounty area?(5points) (a)About $ 81, 000
(b)About $ 83,000
(c)About $ 85, 000
(d)About $ 87, 000
(e)About $ 89, 000 9.The following chart shows the result of disease A test developed by Jean medical company.
Each number in the chart indicates the number of people. For example, 7 people have the
disease A but test negative. Have the disease A Do not have the disease A l Test Positive as Test Negative 7 ! Statistical studyindicates that Pr(Have the disease AlTest Positive)=—g—g and Pr(Have the disease A)=§%‘§. What is the best estimate for the value of x and y? Write your answer.(6points) 10.There is one red ball, one blue ball and one Whitehall in a. bag. Two students pick
a ball each and after each pick, the students keep the ball. What is the probability of the
ﬁrst student picking a red ball or the second student picking a red ball?(4points) VIN) (a) (b) a (c) ‘ (d) “a (e) ODIN) CH llBucky has a bin with 5 markers; 2 red, 1 black and 2 yellow.
He picks one marker and puts it back to the bin. After that, he picks a second marker.
What is the probability of Bucky picking a red marker on the ﬁrst pick and a black marker on the second?(4points) (d) is, (e) % r\
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5,er 0° <a> (b) 12A sock drawer contains two red, one blue, one White and one gray sock. What is the
probability that you will pick a red sock on the ﬁrst try and another red sock on the second try? The ﬁrst sock picked is not put back in the drawer.
Write your answer.(5points) 13A teacher gives a 10—pointtest to a class of 9 children. All scores are integers(wh01e
numbers) such as 3,4 ,5 etc. Nobody got 0 point and 10 points either. If the median is 7 then What is the lowest possible average?(5points) (a) £2? lb) 37 (c) (d) s (e) s 14.The following is a graph of a quadratic function g(x) = A  (x2 —— 5m + 4)(A times
(:32 — 5x + 4)) for some constant Alf the minimum of the function g(:c) is ~18, then What is the value of A?(6points) (a) 2 (b) 4 (c) 6 (d) 8 (e) 10 15.John’s shoe factory produces boots. It costs $23 to produce a pair of boots. And
also, there is a. ﬁxed cost $13, 000 no matter how many pairs of boots they produce.(The
ﬁxed cost needs to be paid only once regardless of the number of boots produced.) If they
sell a pair of boots for $49, how many pairs do they have to sell to break even?(5points) (a) 350 (b) 400 (c) 450 (d) 500 (e) 550 Part II. Long answer questions! 0 You should Show all the work including your answer. 0 There are 3 questions. 1.(1)Ca1cu1ate I
1+2+3+~‘+998+999+1000 by using the proof of arithmetic series.(10points) (2)8antiago opened a new bank account on March 1, 2007 to save money for his sistefs
birthday present. The account earns 3.5% interest at the endof every month. Santiago will
make a payment of $A into the account at the beginning of every month from March 17
2007. If the account balance on December 31,2007 is $400 then what is Santiago’s monthly
payment into the account? In other wordsﬁnd the approximate value of A.(He does not make any Withdrawal between March 1,2007 and December 31,2007.)(15points)
(Note:1.0359 % 1.3629, 1.03510 % 1.4106, 1.03511 % 1.46) 2.Keily is trying to build a fence around her garden. The fence should be a rectangle.
She wants to make the perimeter of fence300 ft.
(1) Write the area A of the fence as a function of W where W is the width of the fence .(6points) (2) Sketch the graph of the function A = A(W) that you found in 2(1).(10points) 10 (3) Find the dimension of the fence to maximize the area of the fence.And also ﬁnd the
maximum area of the fence.(4points) 3. There are two unfair sixsided dice . But one of them is white and the other is yel—
10W. Let. ((1,1)) be a pair of numbers on the two dice Le, (a, b)=(number on the White die, number
on the yellow die). Suppose that Pr(1) = :11 and Pr(2) = Pr(3) = Pr(4) = Pr(5) = Pr(6)
for each die. Calculate Pr(a  b = 6 [ a + b = 7). (30points) ' ...
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This note was uploaded on 08/08/2008 for the course MATH 132 taught by Professor Bae during the Spring '07 term at Wisconsin.
 Spring '07
 BAE
 Math

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